Further notes: I tried the password+key file scenario using a key file generated by KeePass 1.24, and KeePassDroid still couldn't open the database (with the correct password and key file). Nor did it work with the key-file-only scenario (with either key file type: existing or generated).

(I still haven't tried generating a key file with KeePassDroid and seeing whether that works with KeePass itself, but I am not enamored with the dependency on my Android device).